<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
<title>Javascript implementation of Steven Fortune's algorithm to compute Voronoi diagrams: Demo 5</title>
<meta name="Keywords" lang="en" content="voronoi, fortune, javascript, raymond hill"/>
<!--[if lte IE 8]><script type="text/javascript" src="excanvas/excanvas.compiled.js"></script><![endif]-->
<script type="text/javascript" src="rhill-voronoi-core.min.js"></script>
<script type="text/javascript" src="QuadTree.js"></script>
<style type="text/css">
body {font-family:tahoma,verdana,arial;font-size:13px;margin:0;padding:0}
body > div {margin-left:4px;margin-right:4px;}
body > div > div {margin:0;border:1px solid #ccc;border-top:0;padding:4px;}
h1 {margin:0 0 0.5em 0;padding: 4px 5em 4px 4px;font:bold large sans-serif;background-color:#c9d7f1;}
h4 {font-size:14px;margin:0.5em 0 0 0;border:0;border-bottom:solid 1px #c9d7f1;padding:2px;background-color:#e5ecf9;}
#canvasParent {margin-top:0;margin-bottom:1em;padding:0;border:0}
#voronoiCode {font:11px monospace;overflow:auto;color:#666;}
#voronoiCode span {color:green;font-weight:bold;}
</style>
<script id="script" type="text/javascript">
var VoronoiDemo = {
	voronoi: new Voronoi(),
	diagram: null,
	margin: 0.1,
	canvas: null,
	bbox: {xl:0,xr:800,yt:0,yb:600},
	sites: [],
	timeoutDelay: 100,

	init: function() {
		this.canvas = document.getElementById('voronoiCanvas');
		this.randomSites(100,true);
		},

	clearSites: function() {
		this.compute([]);
		},

	randomSites: function(n, clear) {
		var sites = [];
		if (!clear) {
			sites = this.sites.slice(0);
			}
		// create vertices
		var xmargin = this.canvas.width*this.margin,
			ymargin = this.canvas.height*this.margin,
			xo = xmargin,
			dx = this.canvas.width-xmargin*2,
			yo = ymargin,
			dy = this.canvas.height-ymargin*2;
		for (var i=0; i<n; i++) {
			sites.push({x:self.Math.round((xo+self.Math.random()*dx)*10)/10,y:self.Math.round((yo+self.Math.random()*dy)*10)/10});
			}
		this.compute(sites);
		// relax sites
		if (this.timeout) {
			clearTimeout(this.timeout)
			this.timeout = null;
			}
		var me = this;
		this.timeout = setTimeout(function(){
			me.relaxSites();
			}, this.timeoutDelay);
		},

	relaxSites: function() {
		if (!this.diagram) {return;}
		var cells = this.diagram.cells,
			iCell = cells.length,
			cell,
			site, sites = [],
			again = false,
			rn, dist;
		var p = 1 / iCell * 0.1;
		while (iCell--) {
			cell = cells[iCell];
			rn = Math.random();
			// probability of apoptosis
			if (rn < p) {
				continue;
				}
			site = this.cellCentroid(cell);
			dist = this.distance(site, cell.site);
			again = again || dist > 1;
			// don't relax too fast
			if (dist > 2) {
				site.x = (site.x+cell.site.x)/2;
				site.y = (site.y+cell.site.y)/2;
				}
			// probability of mytosis
			if (rn > (1-p)) {
				dist /= 2;
				sites.push({
					x: site.x+(site.x-cell.site.x)/dist,
					y: site.y+(site.y-cell.site.y)/dist,
					});
				}
			sites.push(site);
			}
		this.compute(sites);
		if (again) {
			var me = this;
			this.timeout = setTimeout(function(){
				me.relaxSites();
				}, this.timeoutDelay);
			}
		},

	distance: function(a, b) {
		var dx = a.x-b.x,
			dy = a.y-b.y;
		return Math.sqrt(dx*dx+dy*dy);
		},

	cellArea: function(cell) {
		var area = 0,
			halfedges = cell.halfedges,
			iHalfedge = halfedges.length,
			halfedge,
			p1, p2;
		while (iHalfedge--) {
			halfedge = halfedges[iHalfedge];
			p1 = halfedge.getStartpoint();
			p2 = halfedge.getEndpoint();
			area += p1.x * p2.y;
			area -= p1.y * p2.x;
			}
		area /= 2;
		return area;
		},

	cellCentroid: function(cell) {
		var x = 0, y = 0,
			halfedges = cell.halfedges,
			iHalfedge = halfedges.length,
			halfedge,
			v, p1, p2;
		while (iHalfedge--) {
			halfedge = halfedges[iHalfedge];
			p1 = halfedge.getStartpoint();
			p2 = halfedge.getEndpoint();
			v = p1.x*p2.y - p2.x*p1.y;
			x += (p1.x+p2.x) * v;
			y += (p1.y+p2.y) * v;
			}
		v = this.cellArea(cell) * 6;
		return {x:x/v,y:y/v};
		},

	compute: function(sites) {
		this.sites = sites;
		this.voronoi.recycle(this.diagram);
		this.diagram = this.voronoi.compute(sites, this.bbox);
		this.updateStats();
		this.render();
		},

	updateStats: function() {
		if (!this.diagram) {return;}
		var e = document.getElementById('voronoiStats');
		if (!e) {return;}
		e.innerHTML = '('+this.diagram.cells.length+' Voronoi cells computed from '+this.diagram.cells.length+' Voronoi sites in '+this.diagram.execTime+' ms &ndash; rendering <i>not</i> included)';
		},

	render: function() {
		var ctx = this.canvas.getContext('2d');
		// background
		ctx.globalAlpha = 1;
		ctx.beginPath();
		ctx.rect(0,0,this.canvas.width,this.canvas.height);
		ctx.fillStyle = 'white';
		ctx.fill();
		ctx.strokeStyle = '#888';
		ctx.stroke();
		// voronoi
		if (!this.diagram) {return;}
		// edges
		ctx.beginPath();
		ctx.strokeStyle = '#000';
		var edges = this.diagram.edges,
			iEdge = edges.length,
			edge, v;
		while (iEdge--) {
			edge = edges[iEdge];
			v = edge.va;
			ctx.moveTo(v.x,v.y);
			v = edge.vb;
			ctx.lineTo(v.x,v.y);
			}
		ctx.stroke();
		// sites
		ctx.beginPath();
		ctx.fillStyle = '#44f';
		var sites = this.sites,
			iSite = sites.length;
		while (iSite--) {
			v = sites[iSite];
			ctx.rect(v.x-2/3,v.y-2/3,2,2);
			}
		ctx.fill();
		},
	};
// -->
</script>
</head>
<body onload="VoronoiDemo.init();">
<a href="https://github.com/gorhill/Javascript-Voronoi"><img style="position: absolute; top: 0; right: 0; border: 0;" src="https://s3.amazonaws.com/github/ribbons/forkme_right_red_aa0000.png" alt="Fork me on GitHub"></a>
<h1>Javascript implementation of Steven Fortune's algorithm to compute Voronoi diagrams<br/>Demo 5: Lloyd's relaxation</h1>
<div id="divroot" style="width:800px;">
<p style="margin-top:0;margin-bottom:0"><a href="/voronoi/rhill-voronoi.html">&lt; Back to main page</a><ul style="margin-top:0">
<li><a href="rhill-voronoi-demo1.html">Demo 1: measuring peformance</a>
<li><a href="rhill-voronoi-demo2.html">Demo 2: a bit of interactivity</a>
<li><a href="rhill-voronoi-demo3.php">Demo 3: Fancy tiling</a>
<li><a href="rhill-voronoi-demo4.html">Demo 4: Looking up a Voronoi cell using a quadtree</a>
<li><b>Demo 5: Lloyd's relaxation</b>
<li><a href="http://www.raymondhill.net/blog/?p=458#comments">Comments</a>
</ul></p>
<h4 class="divhdr">Sites generator</h4>
<div class="divinfo" id="voronoiGenerator">
<input type="button" value="Generate" onclick="VoronoiDemo.randomSites(parseInt(document.getElementById('voronoiNumberSites').value,10),true);VoronoiDemo.render();"/> or <input type="button" value="Add" onclick="VoronoiDemo.randomSites(parseInt(document.getElementById('voronoiNumberSites').value,10),false);VoronoiDemo.render();"/><input id="voronoiNumberSites" type="text" value="100" size="5" maxlength="5"/> sites randomly (Warning: performance might suffer the more sites you add.)
<br/><input id="voronoiClearSites" type="button" value="Clear all sites" onclick="VoronoiDemo.clearSites();VoronoiDemo.render();"/>
</div>
<h4 class="divhdr">Canvas <span id="voronoiStats" style="font:normal 11px sans"></span> <span style="font:normal 11px sans"></h4>
<div id="canvasParent">
<noscript>You need to enable Javascript in your browser for this page to display properly.</noscript>
<canvas id="voronoiCanvas" width="800" height="600"></canvas>
<div id="voronoiNoCanvasAlert" style="display:none;padding:1em;background-color:#fcc;color:black;">
<p>Your browser doesn't support the HTML5 &lt;canvas&gt; element technology.</p>
<p>See <a target="_blank" href="http://en.wikipedia.org/wiki/Canvas_(HTML_element)">Wikipedia</a> for information on which browsers support the <u>HTML5 &lt;canvas&gt;</u> technology.</p>
</div>
</div>
<h4 class="divhdr">Javascript source code for this page</h4>
<div class="divinfo" id="voronoiCode">
<pre>
<span>&lt;script type=&quot;text/javascript&quot; src=&quot;<a href="rhill-voronoi-core.js" target="_blank">rhill-voronoi-core.js</a>&quot;&gt;&lt;/script&gt;</span>
...
<div id="scriptContainer"></div>
...
</pre>
</div>
</div>
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